Question

Use the worked example above to help you solve this problem. A merry-go-round modeled as a disk of mass M 7.00 x 101 kg and radius R 2.40 m is rotating in a horizontal plane about a frictionless vertical axle (see figure). (a) After a student with mass m 86.0 kg jumps onto the merry-go-round, the system's angular speed decreases to 1.95 rad/s. If the student walks slowly from the edge toward the center, find the angular speed of the system when she reaches a point 0.450 m from the center. 5.64 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error rad/s (b) Find the change in the system's rotational kinetic energy caused by her movement to the center. 2613.05 Your response differs from the correct answer by more than 10%. Double check your calculations. (c) Find the work done on the student as she walks to r 0.450 m 613.39 EXERCISE HINTS: GETTING STARTED I I'M STUCK! Use the values from the PRACTICE IT section to answer this exercise. (a) Find the angular speed of the merry-go-round before the student jumped on, assuming the student didn't transfer any momentum or energy as she jumped on the merry-go-round 6.143 Angular momentum is conserved. There are some useful expressions in the example, but do not use all of them, since only some basic ones are valid. rad/s (b) By how much did the kinetic energy of the system change when the student jumped on? Notice that energy is lost in this process, as should be expected, since it is essentially a perfectly inelastic collision. KE KE, 2967.38 You should assume that the student has no kinetic energy before jumping onto the merry-go round. Keep in mind that the initial angular speed in the example is the final angular speed in this exercise. J

Answer 1

R- 2.4m 쫓 R2 4. 295T 0.5 + 1:22857 2054-Rod se Change in lti nelie 2MR2 -261-6 0.54 3192112 ) =2831.4111 2 「1+ 2(86).le.95). 6-7 Anadkesi, 0 - 40) 2-4% [69 looo inemangH -3254.01T